{"id":5159,"date":"2025-07-14T07:49:39","date_gmt":"2025-07-14T06:49:39","guid":{"rendered":"https:\/\/pcool.dyndns.org\/?page_id=5159"},"modified":"2025-07-14T15:28:41","modified_gmt":"2025-07-14T14:28:41","slug":"different-correlation-coefficients","status":"publish","type":"page","link":"https:\/\/pcool.dyndns.org\/index.php\/different-correlation-coefficients\/","title":{"rendered":"Different Correlation Coefficients"},"content":{"rendered":"\n<p>Different correlation coefficients have been described. All of them have a range from -1 to +1. <\/p>\n\n\n\n<p>The most common is the <strong>Pearson correlation coefficient<\/strong> that is used when data roughly conform to a normal distribution and it exams a <strong>linear relationship<\/strong> between the two variables.<\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\( r = \\frac{n(\\Sigma xy) &#8211; (\\Sigma x)(\\Sigma y)}{\\sqrt{[n(\\Sigma x^2) &#8211; (\\Sigma x)^2][n(\\Sigma y\\\n^2) &#8211; (\\Sigma y)\\\n^2]}} \\)<script src=\"https:\/\/pcool.dyndns.org\/wp-includes\/js\/dist\/hooks.min.js?ver=dd5603f07f9220ed27f1\" id=\"wp-hooks-js\"><\/script>\n<script src=\"https:\/\/pcool.dyndns.org\/wp-includes\/js\/dist\/i18n.min.js?ver=c26c3dc7bed366793375\" id=\"wp-i18n-js\"><\/script>\n<script id=\"wp-i18n-js-after\">\nwp.i18n.setLocaleData( { 'text direction\\u0004ltr': [ 'ltr' ] } );\n\/\/# sourceURL=wp-i18n-js-after\n<\/script>\n<script  async src=\"https:\/\/cdnjs.cloudflare.com\/ajax\/libs\/mathjax\/2.7.7\/MathJax.js?config=TeX-MML-AM_CHTML\" id=\"mathjax-js\"><\/script>\n<\/div>\n\n\n\n<p>The <strong>Spearman correlation coefficient<\/strong> is used for ranked data that can&#8217;t be modelled with a normal distribution. It does however assume data are monotonic (going in the same direction)and can be used for continuous and ordinal data.<\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\( \u03c1 = 1 &#8211; \\frac{6 \\sum d_i^2}{n(n^2 &#8211; 1)} \\)<\/div>\n\n\n\n<p>The <strong>Kendall correlation coefficient<\/strong> doesn&#8217;t assume any distribution within the data and is very general.<\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\"><\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\(  \\tau = 1-{\\frac {2({\\text{number of discordant pairs}})}{n \\choose 2} }\\) <\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\"><\/div>\n\n\n\n<p>Please refer to the <a href=\"https:\/\/pcool.dyndns.org\/index.php\/do-storks-deliver-babies\/\" data-type=\"page\" data-id=\"5096\">stork paper<\/a> for an example of calculating the different correlation coefficients.<\/p>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Different correlation coefficients have been described. All of them have a range from -1 to +1. The most common is the Pearson correlation coefficient that is used when data roughly conform to a normal distribution and it exams a linear relationship between the two variables. The Spearman correlation coefficient is used for ranked data that [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-5159","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pcool.dyndns.org\/index.php\/wp-json\/wp\/v2\/pages\/5159","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pcool.dyndns.org\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/pcool.dyndns.org\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/pcool.dyndns.org\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/pcool.dyndns.org\/index.php\/wp-json\/wp\/v2\/comments?post=5159"}],"version-history":[{"count":4,"href":"https:\/\/pcool.dyndns.org\/index.php\/wp-json\/wp\/v2\/pages\/5159\/revisions"}],"predecessor-version":[{"id":5233,"href":"https:\/\/pcool.dyndns.org\/index.php\/wp-json\/wp\/v2\/pages\/5159\/revisions\/5233"}],"wp:attachment":[{"href":"https:\/\/pcool.dyndns.org\/index.php\/wp-json\/wp\/v2\/media?parent=5159"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}